There is well known a control apparatus for a vehicular drive system provided with a vehicle driving electric motor, and a fluid-operated power transmitting device interposed between the electric motor and drive wheels of a vehicle. Patent Document 1 discloses an example of such a control apparatus for a vehicular drive system. This control apparatus is configured to reduce an amount of supply of an electric energy to the above-indicated electric motor for a predetermined length of time, if the electric motor has been kept operated for more than a predetermined period of time in an operating state of the vehicular drive system wherein a rate of change of an operating speed of the electric motor is lower than a predetermined value while a drive force generated by the electric motor is larger than a predetermined value. This reduction of the electric energy supply amount makes it possible to prevent a rise of a temperature of the electric motor or a power control device including an inverter, which is connected to the electric motor.